JTAM (Jurnal Teori dan Aplikasi Matematika)
Journal Title JTAM (Jurnal Teori dan Aplikasi Matematika) <table class="data" style="border: 0px; border-spacing: 0px; font-size: 12px; color: #222222; font-family: Tahoma, Verdana, Arial, Helvetica, sans-serif; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-style: initial; text-decoration-color: initial;" width="100%" bgcolor="#f0f0f0"> Initials JTAM Frequency 4 issues per year (January, April, July & October) DOI prefix 10.31764 by Print ISSN 2597-7512 Online ISSN 2614-1175 OAI Address http://journal.ummat.ac.id/index.php/jtam/oai Editor-in-Chief Assist. Prof. Dr. Syaharuddin [Scopus ID 57217864595] Status Accredited (Sinta 2) | No. 0173/C3/DT.05.00/2025 Valid: Volume 8 Issues 2 2024 - Volume 13 Issues 1 2029 Contact jtam.ummat@gmail.com Publication October 2017 Publisher Universitas Muhammadiyah Mataram JTAM (Jurnal Teori dan Aplikasi Matematika) publishes high-quality, peer-reviewed research that bridges theoretical mathematics and interdisciplinary applications. The journal emphasizes the integration of computation, modeling, educational innovation, and cultural perspectives to advance mathematical understanding and its role in sustainable development, digital transformation, and inclusive scientific literacy across global and local contexts. JTAM (Jurnal Teori dan Aplikasi Matematika) focuses on the following research areas: Computational and Applied Mathematics. This area covers original research on mathematical modeling, numerical methods, simulation, and computational analysis for solving real-world problems. It includes applied mathematics studies addressing complex systems in physics, engineering, finance, epidemiology, environmental science, and socio-technical systems. Topics include numerical optimization, dynamical systems, computational fluid dynamics, inverse problems, and simulation-based modeling that establish strong links between mathematical theory and practical applications. Emphasis is given to research contributing to algorithmic innovation, computational efficiency, and multidisciplinary modeling frameworks. Mathematical Foundations, Modeling, and Analytical Approaches in Data Science, Artificial Intelligence, and Machine Learning. This focus highlights the mathematical and analytical foundations of data-driven technologies. It welcomes studies on the formulation, analysis, and validation of algorithms, hybrid intelligent systems, uncertainty modeling (fuzzy, stochastic, or probabilistic), and optimization theory in AI and machine learning contexts. Particular attention is given to works that connect mathematical rigor with AI innovation, such as explainable AI (XAI), mathematical interpretability of neural models, and analytical guarantees of learning algorithms. Applications include healthcare, climate prediction, economics, cybersecurity, and education. Statistical Modeling, Data Analysis, and the Integration of Probabilistic Models with Machine Learning Techniques. This section includes theoretical and applied research in statistics, probability, and stochastic processes, with an emphasis on their integration with modern machine learning methods. Areas of interest include Bayesian inference, time series forecasting, spatial-temporal analysis, uncertainty quantification, and statistical learning theory. The focus is on the fusion of probabilistic and statistical approaches to enhance predictive performance, risk assessment, and data-driven decision-making in complex or uncertain environments. Mathematics Education and Technology Integration in Digital Pedagogy and Computational Thinking. JTAM (Jurnal Teori dan Aplikasi Matematika) supports research advancing mathematics education through digital innovation and technology integration. This includes AI-assisted learning, computational literacy, STEM-based learning models, and interactive e-learning systems that enhance students’ reasoning, problem-solving, and creativity. The journal welcomes design-based research, systematic literature reviews, and data analytics in mathematics education, especially those exploring human–machine interaction, digital pedagogy frameworks, and adaptive learning technologies relevant to the 21st-century classroom. Ethnomathematics, Mathematical Creativity, and Cultural Integration. This area explores the intersection of mathematics, culture, and creativity, fostering a humanistic perspective in mathematical thought. Research topics include ethnomathematics, culturally responsive pedagogy, mathematical semiotics, and local wisdom-based learning. JTAM (Jurnal Teori dan Aplikasi Matematika) encourages works that link mathematical reasoning to art, architecture, traditional games, and indigenous or Islamic values, promoting a deeper understanding of how mathematical ideas evolve through cultural diversity and human creativity.
Authors who publish articles in JTAM (Jurnal Teori dan Aplikasi Matematika) agree to the following terms: Authors retain copyright of the article and grant the journal right of first publication with the work simultaneously licensed under a CC-BY-SA or The Creative Commons Attribution–ShareAlike License. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Modelling Consumer Price Index Effect on 10-year US Treasury Bond Yields using Least Square Spline Approach
Inflation measured by the Consumer Price Index (CPI) is a critical indicator in the government bond market that directly affects the yields of long-term securities such as the 10-year US Treasury Bond. This study is an explanatory quantitative study that aims to examine the complex dynamics of this relationship using the nonparametric least square spline method. The analysis uses monthly CPI data from FRED and 10-year US Treasury bond yield data from Investing.com for the period 2013-2025. This method divides the data into simple polynomial segments that are smoothly connected at transition points (knots), enabling the modelling of nonlinear patterns without assuming an initial curve shape. The analysis results indicate that a first-degree polynomial spline model (piecewise linear) with three knots successfully represents the bond yield response to inflation shocks with R^2 = 86.48%. Model segmentation identified four regimes: (1) Post-crisis recovery phase, with a negative relationship driven by Fed monetary stimulus suppresing yields despite initial inflation emergence; (2) Policy normalization phase, with a positive relationship aligned with monetary tightening in response to moderate inflation; (3) During the COVID-19 pandemic, a negative relationship due to a surge in demand for safe-haven bonds despite rising inflation; (4) Post-pandemic, the relationship turned positive again following the Fed’s aggressive monetary tightening in response to high global inflation. These findings highlight the urgency of regime-based monitoring for investors and policymakers, while contributing concretely to SDG 8 (decent work and economic growth) through the facilitation of appropriate interest rate policies for sustainable macroeconomic stability, and supporting SDG 9 (industry, innovation, and infrastructure) through the identification of inflation patterns that strengthen shock-resistant infrastructure investment planning and financial innovation during turbulent economic transitions.
Copyright (c) 2026 Julia Widiyanti, Safira Salsabila, Dwika Maya Harsanti, Dita Amelia, Marisa Rifada https://creativecommons.org/licenses/by-sa/4.0
Comparing MARS and Binary Logistic Regression to Modelling Hepatitis C Cases using the SMOTE Balancing Method
Hepatitis is an inflammatory liver disease caused by viral infection and remains a major global public health concern, responsible for approximately 1.4 million deaths annually. Egypt is among the countries with the highest prevalence of Hepatitis C. To address this issue and support Goal 3 of the Sustainable Development Goals (SDGs), this study applies a quantitative approach using secondary data to analyze factors influencing Hepatitis C infection in Egypt. Two statistical models Binary Logistic Regression and Multivariate Adaptive Regression Splines (MARS) were compared, with the SMOTE method implemented to correct class imbalance. The dataset consisted of 608 patient observations, initially imbalanced at a ratio of 86.5:13.5, and were balanced to 52.6:47.4 after SMOTE application. The results revealed that the MARS model demonstrated superior predictive performance compared to binary logistic regression. All independent variables were found statistically significant (p < 0.05), except sex. Additionally, all odds ratios were less than 1, indicating a lower probability of Hepatitis C infection relative to non-infection. These findings highlight the relevance of statistical modeling and data-driven strategies in supporting preventive health measures.
Copyright (c) 2026 Nur Chamidah, Aulia Ramadhanti, Azzah Nazhifa Wina Ramadhani, Bimo Okta Syahputra, Jovansha Ariyawan, Ardi Kurniawan https://creativecommons.org/licenses/by-sa/4.0
Dimensionality Reduction Evaluation of Multivariate Time Series of Consumer Price Index in Indonesia
Multivariate time series (MTS) analysis of the Consumer Price Index (CPI) in Indonesia often encounters challenges such as outliers, missing data, and inter-variable correlations. Principal Component Analysis (PCA) is a practical approach for dimensionality reduction; however, its performance may vary depending on the data characteristics. This study is a quantitative comparative study that integrates empirical analysis and Monte Carlo simulation based on a first-order Vector Autoregressive (VAR(1)) model to evaluate three PCA approaches: Classical PCA, Robust PCA (RPCA), and PCA of MTS. These methods were applied to weekly price data of eight strategic food commodities across 70 districts and cities in Indonesia. The evaluation employed three criteria: (1) dimensionality reduction efficiency (empirical and simulation), (2) reconstruction accuracy measured using Root Mean Square Error (RMSE) (empirical), and (3) robustness to outliers and inter-variable correlations (simulation). Empirical results indicate that Classical PCA (lag 1) and RPCA (lag 1) are both efficient and effective in reducing dimensionality with minimal information loss. Using the first three principal components, all three methods were able to explain at least 85% of the total variance, with lag 1 identified as optimal. Simulation results reveal that RPCA (lag 1) provides the most stable and consistent performance in the presence of outliers, while Classical PCA (lag 2) performs better under conditions of high inter-variable correlation and a low proportion of outliers. These findings suggest that robust covariance estimation can improve the accuracy of dimensionality reduction and enhance the stability of multivariate time-series analysis for food price data in Indonesia.
Copyright (c) 2026 Nina Valentika, I Made Sumertajaya, Aji Hamim Wigena, Farit Mochamad Afendi https://creativecommons.org/licenses/by-sa/4.0
Geostatistical Co-Kriging Approach for Estimating Total Coliform Bacteria in the Rivers of DKI Jakarta
Spatial statistics and geostatistics are essential for analyzing spatially distributed data, particularly in environmental studies where data gaps are prevalent. However, limited studies have applied multivariate geostatistical approaches, particularly Co-Kriging (CK), to assess microbial contamination in tropical urban river systems, where pollution patterns are highly variable and data gaps are frequent. This study employs CK, a multivariate geostatistical interpolation technique, to estimate Total Coliform Bacteria concentrations in the rivers of DKI Jakarta, Indonesia. Total Coliform Bacteria served as the primary variable, with Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD) incorporated as secondary variables. A total of 120 sampling points were analyzed, with data collected by Dinas Lingkungan Hidup DKI Jakarta during the second monitoring period in June 2022. Semivariogram modelling identified the Gaussian model as the best fit, yielding the lowest root mean square error (RMSE) of 11.468, which performed better than both the Spherical and Exponential models. Model performance was further evaluated through Leave-One-Out Cross-Validation (LOOCV), in which one data point was systematically removed and re-estimated in multiple iterations to calculate the residuals and assess model accuracy. The CK analysis was performed using RStudio software. CK predictions closely matched observed concentrations, demonstrating strong model performance. At unsampled locations, the estimated mean Total Coliform Bacteria concentration was 7.711 × 10⁶ MPN/100 ml with a standard deviation of 4.406 × 10⁶ MPN/100 ml. The high variance indicates substantial spatial heterogeneity, likely driven by data outliers, weak spatial autocorrelation in COD, and low correlations between Total Coliform–COD and BOD–COD pairs. These findings highlight the potential of geostatistical CK to provide reliable spatial predictions of microbial contamination in urban river systems, thereby supporting evidence-based water quality monitoring and management in densely populated regions. The insights generated in this study can help environmental authorities in DKI Jakarta optimize monitoring strategies, prioritize pollution hotspot interventions, and strengthen urban river health management to protect public health and guide sustainable urban water governance.
Copyright (c) 2026 Salwa Salsabila, Dwi Agustin Nuriani Sirodj https://creativecommons.org/licenses/by-sa/4.0
Synchonized DAMRI Public Tourist Transportation Route Design using Max-Plus Algebra
The transportation system is a crucial infrastructure for supporting connectivity between each National Strategic Tourist Area (NSTA) tourist destination of Yogyakarta. Management of transportation network and scheduling departure of transportation services are not yet optimal. This study aims to design a synchronized DPTT route and schedule that covers the entire service area using max-plus algebra. This type of study is applied research. The scheduling problem will focus on determining the number of fleets serving all routes with departure periods below 60 minutes. This research was conducted through literature review, field observations and online maps using Google Maps, and computation using the Scilab program. The results show that time travel between 8 tourist destinations are organized into a strongly connected directed graph with 20 routes. Departures are modeled as a linear discrete-event system over max-plus algebra. Computation in Scilab produce a baseline departure period of 90 minutes. We evaluate by adding 2, 8, 10, or 12 of buses by reinforcing the longest route. The simulation shows that the addition of 10 and 12 buses in certain section can reduce the departure period to 56 and 48 minutes respectively. The results demonstrate that targeted fleet additions and network reconnection, guided by max-plus synchronization, can substantially improve service regularity and passenger connectivity.
Copyright (c) 2026 Krisma Yonantha, Dewa Putu Wiadnyana Putra, Marcellinus Andy Rudhito https://creativecommons.org/licenses/by-sa/4.0
The Probability Model of Earthquake Frequency in the Enggano Segment using Poisson Mixture Models
An earthquake is a natural disaster that occurs suddenly resulting in numerous casualties, such as loss of life and property. Bengkulu Province is among the provinces affected by severe earthquakes. Studies on probability models for the frequency of earthquake events in Bengkulu Province are still scarce, as outlined in the 2017 book “Map of Sources and Hazards of Indonesian Earthquakes.” This research uses Poisson mixture models to build a probability model for the frequency of earthquake events in the Enggano segment, located in the coastal area of Bengkulu Province. .. The phases of model building are the model diagnosis phase, testing the dispersion state relative to the Poisson distribution, testing the dependence of research data on time variables using the Ljung-Box test, and testing the criteria for selecting the best model using the Bayesian Tests Measures of Information Criterion (BIC) and Akaike Information Criterion (AIC). Annual earthquake frequency data from January 1, 1971, to December 31, 2022, were retrieved from the USGS catalog of data on the frequency of major earthquakes with a magnitude of Mw ≥ 4.40, which occurred a total of 633 times. After completing the model building phase, the AIC and BIC values for each model were determined by determining the number of unobserved groups. Both Poisson mixture models and Poisson hidden Markov models produced the same number of unobserved groups of 3 groups with AIC=302.91 and BIC=324.38.
Copyright (c) 2026 Siska Yosmar, Ramya Rachmawati, Septri Damayanti, Jose Rizal https://creativecommons.org/licenses/by-sa/4.0
Application on Hypergraph in Vigenere Chiper
Message protection remains a major focus in the field of cryptography. This study proposes a new development on the Caesar cipher algorithm by utilizing hypergraph as a keystream generation source. The research designs a super (a,d)-hyperedge antimagic total labeling method applied to three hypergraph structures (Volcano, Semi Parachute, and Comb) to generate the keystream. Security is evaluated using four mechanisms: brute force analysis, processing time, ciphertext character distribution, and ciphertext bit size. The findings prove that the hypergraph based approach is robust against brute force attacks, improve memory and time efficiency. Quantitatively, the Comb hypergraph demonstrates the best efficiency, achieving an encryption time of 0.0030 seconds for 512 bytes and superior storage efficiency (e.g., 136 bytes for 16 bytes ), outperforming the Semi Parachute and Volcano structures. The main contributions include the hypergraph labeling-based keystream generation algorithm, dynamic block key construction, and a Vigenere protocol that is more adaptive to storage constraints and computationally efficient..
Copyright (c) 2026 Okta Endri Asari, Dafik, Robiatul Adawiyah, Arika Indah Kristiana, Rafiantika Megahnia Prihandini https://creativecommons.org/licenses/by-sa/4.0
Application of Kernel Nonparametric Biresponse Regression with the Nadaraya-Watson Estimator in Poverty Analysis in South Sulawesi
Poverty is a complex social issue that requires in-depth analysis to identify its contributing factors. South Sulawesi, as one of the provinces in Indonesia, continues to face various challenges in poverty alleviation. This study is a quantitative research that aims to model the poverty rate and poverty severity index using a biresponse nonparametric kernel regression with the Nadaraya-Watson estimator and Gaussian kernel function. The analysis is based on 2024 data form the Central Bureau of Statistics (BPS), which includes poverty indicators as response variables and socio-economic factors, processed using R Studio 2025. The nonparametric biresponse kernel regression analysis yielded optimal bandwidths of h_1=0,188; h_2=0,083; h_3=0,159; and h_4=0,028. Model accuracy is demonstrated by a Generalized Cross-Validation (GCV) value of 5.515 and a Mean Squared Error (MSE) of 0.585, indicating high stability and low prediction error. The model demonstrates adaptive accuracy in simultaneously modeling the two response variables and highlights the strength of kernel-based biresponse regression as an evidence-based tool for policymakers to design targeted, region-specific poverty alleviation strategies.
Copyright (c) 2026 Hartina Husain, Muhammad Rifki Nisardi, Ryo Hartawan Sasolo https://creativecommons.org/licenses/by-sa/4.0
Transformation of Junior High School Mathematics Learning: Integration of Interactive Student Worksheet and Virtual Reality Based on Deep Learning Approach
Mathematics learning in junior high schools still faces challenges in building active student engagement, deep conceptual understanding, and the application of technology during the learning process. This study aims to describe the transformation of the implementation of mathematics learning in junior high schools through the integration of interactive Student Worksheets (LKPD) and Virtual Reality (VR) based on the Deep Learning approach. The research employed a qualitative descriptive method, with data collected through classroom observations and interviews involving four classes of grade VII students and interviews with four grade VII mathematics teachers from four different junior high schools. Before implementation, all research instruments including the interactive LKPD, VR media assisted by Artsteps, observation sheets, and interview guidelines were validated by three experts in mathematics education and educational technology, and the results were categorized as very valid. Data were analyzed using the Miles and Huberman model, consisting of four stages: data collection, data reduction, data presentation, and conclusion drawing. The result of this study is that the application of the Deep Learning approach supported by interactive LKPD and VR media received a positive response from teachers and students. Interactive LKPD and VR Media effectively support the Deep Learning stages, namely (1) Introduction of material with context, (2) In-depth presentation of material, (3) Project-based assignments, (4) Discussion and collaboration, (5) In-depth reflection, (6) Provision of constructive feedback, (7) Competency-based assessment (8) Use of technology in learning, (9) Independent learning and self-regulation, (10) Evaluation and development on an ongoing basis. The implementation of learning is in line with the principles of Deep Learning, namely knowledge connectedness, active involvement, critical and reflective thinking, problem-based learning, collaboration, and intrinsic motivation; and also in line with the Deep Learning learning experience, namely understanding, applying and reflecting. These results show that the integration of interactive LKPD and VR media can be an effective strategy to transform mathematics learning at the junior high school level.
Copyright (c) 2026 Vita Istihapsari, Jaka Wijaya Kusuma https://creativecommons.org/licenses/by-sa/4.0
Statblithz Game Media Development to Train Students' Mathematical Problem-Solving Skills
Mathematical problem-solving skills are essential for students to succeed in the 21st century, yet many struggle to apply mathematical concepts in real-life situations. This research addresses the need for innovative learning media by developing Statblithz Game, an educational game designed to train and enhance students’ mathematical problem-solving abilities. The study employed a Research and Development approach using the ADDIE model, involving stages of analysis, design, development, implementation, and evaluation. Participants included middle school students who engaged with the prototype and provided feedback through questionnaires, expert validations, and pre- and post-tests measuring problem-solving performance. The results indicated that Statblithz Game is highly feasible, with expert validation scores averaging 89%. Moreover, students’ problem-solving test scores improved by an average of 25% after using the game. In conclusion, the Statblithz Game effectively enhances mathematical problem-solving skills and offers an engaging alternative to traditional mathematics instruction. The impact of this research lies in providing educators with an innovative and interactive tool that can foster critical thinking and improve student learning outcomes in mathematics.
Copyright (c) 2026 Ani Afifah, Alya Wulandari, Rani Darmayanti, Paulo Vitor da Silva Santiago, Samuel Karim https://creativecommons.org/licenses/by-sa/4.0
Analysis Comparison of BiLSTM and BiGRU Models for Aircraft Visibility Prediction
Severe weather conditions such as fog and heavy precipitation pose significant threats to aviation safety. Accurate prediction of aircraft visibility is therefore essential to support operational decision-making and reduce the likelihood of accidents. This study aims to compare and evaluate the performance of two bidirectional deep learning models, BiLSTM and BiGRU, in predicting aircraft visibility using historical meteorological data from BMKG Juanda Sidoarjo. The novelty of this research lies in applying and comparing bidirectional recurrent architectures for visibility prediction, an approach rarely explored in aviation meteorology, to assess their capability in capturing temporal dependencies within time-series visibility patterns. Both models were trained using hyperparameter tuning, with the best configuration obtained from a 24-hour input window, batch size of 32, 64 neurons, a dropout rate of 0.1, and 100–200 epochs. The dataset was divided into training and testing sets (80:20), and model performance was evaluated using Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) to assess both predictive accuracy and computational efficiency. The results indicate that while BiLSTM achieved slightly higher accuracy, BiGRU demonstrated superior overall efficiency, obtaining competitive error metrics (MSE = 1.50 × 10⁶, RMSE = 1,223.5, MAPE = 19.35%) compared to BiLSTM (MSE = 1.58 × 10⁶, RMSE = 1,258.1, MAPE = 19.50%). BiGRU’s advantage lies in its simpler structure and faster computation, which reduce training complexity without sacrificing forecast accuracy. Overall, this research contributes to the development of efficient bidirectional time-series models for aviation meteorology, offering a practical framework for real-time visibility forecasting in computationally limited environments. The balance between accuracy, speed, and model simplicity makes BiGRU a more scalable and applicable choice for enhancing flight safety operations.
Copyright (c) 2025 Nayla Fitriyatus Saidah, Nurissaidah Ulinnuha, Yuniar Farida https://creativecommons.org/licenses/by-sa/4.0
Mathematics Learning Activities using Vignette Activity Sequence (VAS) and Braille Clock for Visually Impaired Students
Mathematics learning for students with visual impairments is often challenging because many concepts are visual in nature, including units of time that require an understanding of the spatial position of clock hands. This condition requires a more concrete, tactile, and structured learning approach so that concepts can be understood meaningfully. This study aims to describe how Vignette Activity Sequence (VAS) based mathematics learning with braille clock media supports the understanding of time unit concepts in students with visual impairments. This study uses a double case study qualitative approach with two subjects, one with low vision and one with full blind student, selected through purposive sampling. The intervention lasted for one month through a series of VAS sessions that integrated contextual narratives, tactile exploration, and manipulative activities using braille clocks. Data were obtained through observation, semi-structured interviews, and documentation, then analyzed using the Miles and Huberman interactive model. The results showed that VAS helped both subjects understand the relationship between the movement of the short hand and the rotation of the long hand, albeit at different rates of development. The low vision subject was quicker to recognize numbers and understand time units, while the totally blind subject showed gradual improvement in tactile orientation and number touching strategies. Both experienced increased accuracy in reading time and moving the clock hands after attending repeated sessions. These findings confirm that the integration of VAS and braille clocks provides an effective and inclusive multisensory learning experience for students with visual impairments.
Copyright (c) 2026 Diva Lailatul Maghfiroh, Nia Wahyu Damayanti https://creativecommons.org/licenses/by-sa/4.0
The Severe Stunting Cases of Children in Central Java Province Explained by Negative Binomial Regression Model
Severe stunting, or very short stature among children, remains a critical public health concern in Central Java Province. Robust statistical modelling is essential to identify the key factors associated with these cases and to guide targeted interventions. This study employs count regression models with an offset variable to analyze the factors influencing severe stunting cases across districts in Central Java. By using 2023 official data in districts level taken from the Ministry of Home Affairs and the Statistics Indonesia, we initially utilize a Poisson regression model in this study. However, due to evidence of overdispersion, a Negative Binomial regression model was adopted. Backward elimination was then applied to obtain the most parsimonious model. The Negative Binomial regression successfully addressed overdispersion. Five factors were identified as having a statistically significant influence on severe stunting cases: (1) the proportion of pregnant mothers with Chronic Energy Deficiency receiving nutritious food supplements, (2) the percentage of toddlers (6-23 months) receiving complementary nutritious food, (3) the proportion of households with access to good sanitation, (4) Gross Domestic Product per capita, and (5) the number of local healthcare facilities. These factors have negative relation to the stunting rates, meaning improving these factors will reduce the rates of severe stunting. The findings provide a validated statistical model for severe stunting and offer clear policy directions. To mitigate severe stunting, local governments should prioritize: enhancing nutritious food support for pregnant mothers and toddlers, improving household sanitation, stimulating local economic growth, and increasing accessibility to healthcare facilities.
Copyright (c) 2026 Rhendy K. P. Widiyanto, Fatkhurokhman Fauzi, Achmad Fauzan, Anang Kurnia https://creativecommons.org/licenses/by-sa/4.0
Learning Trajectory of Whole Numbers using the Context of Muara Enim Melemang Based on Realistic Mathematics Education (PMRI)
Learning whole numbers in the early grades of elementary school often poses challenges because students must understand abstract concepts and represent them symbolically. This study focuses on developing a Local Instructional Theory (LIT) for learning whole numbers using the Muara Enim melemang cultural context within the Pendidikan Matematika Realistik Indonesia (PMRI) framework. The research contributes both to the development of learning theory (LIT) and to improving the effectiveness of culturally based mathematics learning in Indonesian primary schools. The study employed design research (validation study) consisting of three stages: (1) the preliminary design formulated a Hypothetical Learning Trajectory (HLT) through curriculum analysis and contextual task design; (2) the teaching experiment tested the HLT in classroom practice to explore students’ strategies and interactions; and (3) the retrospective analysis compared the HLT and the Actual Learning Trajectory (ALT) to refine the emerging instructional theory. Findings reveal that the predicted HLT aligned with the ALT. Students successfully developed number sense counting, comparing, ordering, and performing simple operations through concrete representations of lemang. Difficulties mainly appeared in symbolic notation, such as using inequality signs and subtraction symbols. The study’s novelty lies in establishing a local culture-based LIT that bridges PMRI principles with ethnomathematics. Practically, it provides a contextual model teachers can adopt to enhance meaningful mathematics learning in early grades.
Copyright (c) 2026 Arbella Sri Marleny M., Zulkardi, Ratu Ilma Indra Putri, Yusuf Hartono https://creativecommons.org/licenses/by-sa/4.0
Modular Coloring of Comb Graph, Lintang Graph, and Butterfly Graph
Given any graph G that contains no isolated vertices, a labeling c is a mapping from its vertex set to the set of integers modulo k (c:V(G)→Z_k) for k≥2, adjacent vertices are allowed to share the same color. The number of color labels of a vertex v (σ(v)), is the number of color labels of the neighborhood of vertex v (N(v)). A labeling c is a modular k-coloring of G if σ(x) ≠ σ(y) in Z_k for all vertices x,y that are neighbors in G. Denoted as mc(G), the modular chromatic number of G is defined as the least integer k that allows for a modular k-coloring of the graph. This research seeks to ascertain the modular chromatic number of the comb graph Cb_n, the lintang graph L_n, and the butterfly graph BF(n). The first step in this research is to define the labeling c, then determine (N(v)). Next, determine the number of color labels from the neighborhood at each vertex with σ(x)≠σ(y) in Z_k for x,y being all neighboring vertices. After the condition σ(x)≠σ(y) in Z_k is satisfied, ascertain mc(G). By performing the same steps on each graph with increasingly larger values of n, a modular coloring pattern will emerge, which is used to formulate the modular coloring formula. This process concludes with the formulation of a modular coloring formula and the determination of the modular chromatic number for comb graph Cb_n, lintang graph L_n, and butterfly graph BF(n). Based on this research, mc(Cb_n)=2, mc(L_n)=2, and mc(BF(n))=3 are obtained.
Copyright (c) 2026 Deby Debora Pramudya, Yudhi, Fransiskus Fran https://creativecommons.org/licenses/by-sa/4.0
Sentiment Analysis of Hotel Reviews in Senggigi using Decision Tree and Support Vector Machine Algorithm
The tourism industry is a rapidly growing sector that significantly contributes to the economy, including Indonesia. One of the popular tourist destinations in Indonesia is Senggigi, located on the island of Lombok. This destination offers high natural and cultural appeal. In the tourism industry, hotels are crucial as primary accommodations for travelers to stay and rest. Tourist reviews on hotel services greatly influence potential visitor’s decisions in selecting the right accommodation. Therefore, sentiment analysis of hotel reviews is essential for understanding customer satisfaction levels and assisting hotel managers in improving service quality. This research applies a comparative quantitative approach using Decision Tree and Support Vector Machine (SVM) algorithms. The dataset consists of 6,920 hotel reviews collected from TripAdvisor platforms through web scraping techniques. Data preprocessing included data cleaning, case folding, tokenization, stop word removal, and stemming to enhance classification performance. Sentiment labels were categorized into positive, neutral, and negative classes. Model performance was evaluated using multiple metrics, including accuracy, precision, recall, and F1-score, to ensure a comprehensive assessment. The word frequency distribution reveals that that accommodation experience and room quality play a crucial role in customer satisfaction. Positive sentiment is dominated by adjectives like great, nice, and beautiful, reflecting pleasant experiences. Negative sentiment is expressed more politely through phrases such as not good or not very nice. Neutral sentiment tends to be descriptive without strong emotional expression. In terms of model performance, SVM outperformed the Decision Tree model, achieving an accuracy of 90%, precision of 91%, recall of 90%, and an F1-score of 85%. In comparison, the Decision Tree achieved an accuracy of 87%, precision of 84%, recall of 87%, and an F1-score of 85%. These findings demonstrate the superior capability of SVM in handling complex and diverse textual data. This study contributes academically by strengthening empirical evidence on the effectiveness of machine learning–based sentiment analysis in the tourism domain and practically by providing actionable insights for hotel managers to improve service quality and customer satisfaction.
Copyright (c) 2026 Lalu Muhammad Reza Suganda Putra, Heri Wijayanto, I Gede Putu Wirarama Wedashwara https://creativecommons.org/licenses/by-sa/4.0
Innovative Mathematics Learning: The Impact of Augmented Reality and Ethnomathematics on Communication Skills
The integration of digital technology with a cultural approach has become an important innovation in mathematics education to enhance meaningful learning. However, there is still limited research combining Augmented Reality (AR) with ethnomathematics to strengthen students' mathematical communication skills. This study aims to analyze the impact of Augmented Reality and ethnomathematics-based learning on students' mathematical communication skills. The study employed an experimental design involving 60 seventh-grade students selected randomly from eight classes at SMP Negeri 6 Langke Rembong, Ruteng, Indonesia, during the 2024/2025 academic year. The research instrument consisted of a five-item mathematical communication test, which was validated through expert judgment and empirical testing, and demonstrated satisfactory reliability based on internal consistency analysis. SPSS and CMA software were used to support data analysis. A t-test was conducted to examine differences in mathematical communication ability between the experimental and control groups after fulfilling prerequisite assumptions. The findings indicate that the integration of AR and ethnomathematics significantly improved students’ ability to express mathematical ideas clearly, both orally and in written form. Additionally, students showed higher levels of cultural engagement and appreciation, which positively contributed to the development of their communication skills. This study recommends the integration of AR and ethnomathematics as a sustainable innovation in mathematics learning and suggests further research to explore its application across diverse mathematical topics and broader educational contexts.
Copyright (c) 2026 Maximus Tamur, Emilianus Jehadus, Potchong M. Jackaria, Nilo Jayoma Castulo, Ayubu Ismail Ngao https://creativecommons.org/licenses/by-sa/4.0
Optimization of Rice Production Forecasting using Hybrid ANN-PSO
Rice production is a critical component in sustaining national food security, especially Indonesia. The availability of sufficient, affordable, and equitable food is a major challenge for Indonesia. One approach to addressing this challenge is by developing reliable and accurate models for predicting food production. In this study, a hybrid approach that combines Artificial Neural Network (ANN) and Particle Swarm Optimization (PSO) algorithms is used to optimize the performance of modeling and prediction of rice production in Central Java, Indonesia. This study uses secondary data in the form of monthly time series data from the Central Java Provincial Statistics Agency (BPS), Meteorology, Climatology, and Geophysics Agency (BMKG), and satellite imagery data with an observation period from January 2019 to December 2024. The input variables in this study include harvested area, precipitation, number of rainy days, atmospheric pressure, wind speed, NDWI, and NDVI while the output variable is rice production in Central Java. The test results using the ANN model provided an RMSE value of 0.1312 and a MSE of 0.0172, while the ANN-PSO model provided an RMSE value of 0.0259 and a MSE of 0.00067. These results indicate that the PSO algorithm is able to optimize the performance of the ANN model in predicting rice production in Central Java.
Copyright (c) 2026 Wahyuni Windasari, Anggit Gusti Nugraheni https://creativecommons.org/licenses/by-sa/4.0
A Daily Transition Analysis of Disaster Events in Riau Islands using Markov Chains: Dominant Disaster Identification and Risk Assessment
Objectives: This study employs a Markov Chain approach to analyze daily disaster transition patterns in the Riau Islands, with the primary objectives of identifying dominant hazards, quantifying long-term disaster risks, and providing evidence-based recommendations for disaster management. Methods: The research utilized daily disaster records from Indonesia’s National Disaster Management Agency (BNPB) for 2024. A dominant state classification approach was applied to handle days with multiple disaster occurrences, followed by the construction of a transition probability matrix and steady-state analysis to determine long-term disaster distribution. Results: The analysis reveals that no disaster conditions represent the most prevalent state in the region. Among actual disasters, wildfires demonstrate the highest persistence, followed by extreme weather events, floods, and landslides. The transition patterns indicate that most disasters occur as isolated events rather than consecutive sequences, though wildfires show a tendency for temporal clustering. Conclusion: The study provides two key contributions. Methodologically, it demonstrates an effective approach for simplifying complex multi disaster daily data. Practically, it offers scientific evidence for prioritizing wildfire management in the Riau Islands while maintaining preparedness for other episodic disasters. These findings support the development of targeted early warning systems and resource allocation strategies for local disaster management agencies.
Copyright (c) 2026 Nahrul Hayati, Andini Setyo Anggraeni, Eko Sulistyono https://creativecommons.org/licenses/by-sa/4.0
Analysis of DHF Patients Based on Laboratory Examination Results with Nonparametric Approach
The dengue virus, which is spread by the Aedes aegypti mosquito, is the cause of Dengue Hemorrhagic Fever (DHF). In the city of Semarang, there was a threefold increase in cases of DHF compared to previous years. This type of research is quantitative research because it produces function that describes the relationship to what extent changes in predictor variable are related to changes in response variable to understand the level of association. Modelling the link between response and predictor factors is the aim of this study. Platelet as the response variable and hemoglobin and leukocyte as the predictor variables, so that the obtained model can be used as a prediction, especially regarding the dynamics of platelet changes influenced by hemoglobin and leukocytes. The pattern of the relationship between platelets and the suspected influencing factors does not form specific pattern, so the Nonparametric Spline method is used in this study. The Spline method is chosen for its flexibility; this model tends to independently seek data estimates, the completion of this study using R software. In the Spline method, there are knot points indicating data changes. The selection of optimum knot points is done by choosing the minimum GCV value The secondary data used came from Roemani Muhammadiyah Hospital's 2023 medical records. The data include platelet count, hemoglobin, and leukocyte. Based on the modeling conducted using truncated spline, the optimum knot points on the linier spline are determined to be 3 knot points with a coefficient determination of 83.58%. The coefficient of determination of 83.58% indicating that 83.58% of the variation in response variable can be explained by predictor variables studied in the regression model. This value indicates that predictor variables have a strong ability to explain changes in response variable.
Copyright (c) 2026 Tiani Wahyu Utami, M. Al Haris, Nadia Khoirunnafisa Salma https://creativecommons.org/licenses/by-sa/4.0
Modeling Zero-Inflated Poisson Invers Gaussian Regression Bayesian Approach
Deaths due to dengue hemorrhagic fever (DHF) remains one of the most pressing public health issues in Indonesia, especially in urban areas such as Semarang City, which has a high population density and diverse environmental conditions that potentially increase the risk of transmission and death from DHF. This study aims to model the number of DHF in Semarang City using a Bayesian-based Zero-Inflated Poisson Inverse Gaussian Regression (ZIPIGR) approach. The research data was obtained from the Semarang City Health Office and the Central Statistics Agency (BPS) in 2024, with the response variable being the number of DHF deaths and five predictor variables. The data showed overdispersion and a high proportion of zeros (around 50%), indicating the presence of excess zeros in count data with a small sample size. The Bayesian ZIPIGR method was chosen because it can produce more stable parameter estimates than classical methods such as Maximum Likelihood Estimation (MLE), especially for data with complex likelihood functions, small sample sizes, and many zero values. Parameter estimation was performed using Gibbs Sampling simulation in the Markov Chain Monte Carlo (MCMC) framework. The results show that the Bayesian ZIPIGR model performs better than the MLE ZIPIGR model based on the Root Mean Square Error (RMSE) value. Factors that significantly influence DHF mortality are population density, slum area, and number of health workers. These results confirm that regional density and health worker capacity play an important role in increasing the risk of DHF mortality in urban areas. The developed model has been proven to be highly accurate in modeling count data with excess zero characteristics and makes an important contribution to health policy formulation. In practical terms, this model can be used to improve early warning systems and DHF control strategies in densely populated urban areas such as the city of Semarang.
Copyright (c) 2026 Berliana Jannah, Ni Wayan Surya Wardhani, Eni Sumarminingsih https://creativecommons.org/licenses/by-sa/4.0
Arithmetic Adventure: A Role-Playing Game to Support Students’ Mathematical Thinking on Arithmetic Sequences
This study aims to develop an educational Role-Playing Game (RPG) entitled Arithmetic Adventure: The Mystery of Polaria Village to support students’ mathematical thinking on arithmetic sequences. The research employed a Development Research approach using the ADDIE model, which consists of Analyze, Design, Development, Implementation, and Evaluation stages. The subjects were 10th-grade students of SMA Negeri 10 Palembang who had implemented the Merdeka Curriculum. Data were collected through expert validation, student practicality questionnaires, and mathematical thinking ability tests. The results indicated that the RPG obtained an overall average validity score of 4.45, categorized as very valid in terms of content, construct, language, and ICT aspects. Practicality testing showed an average percentage of 86.25%, placing the RPG in the very practical category. Furthermore, the potential effect test revealed that 48.6% of students achieved good, 28.6% very good, and 22.9% fair in mathematical thinking ability, showing improvements in specializing, generalizing, conjecturing, and convincing. These findings demonstrate that Arithmetic Adventure is a valid, practical, and potentially effective educational game for supporting students’ mathematical thinking in arithmetic sequences. The study provides theoretical contributions by reinforcing the role of RPGs in fostering mathematical thinking and practical contributions by offering an innovative alternative medium for mathematics learning.
Copyright (c) 2026 Naqiyyah Nurrosyadah, Ely Susanti, Somakim Somakim https://creativecommons.org/licenses/by-sa/4.0
Process of Proportional Reasoning Students' Errors in Solving Mathematical Problems
Proportional reasoning plays a crucial role in mathematical reasoning, yet many students struggle to coordinate multiplicative relationships when solving mathematical problems. This study aimed to examine the processes behind students’ errors in proportional reasoning and to describe the types of incorrect strategies they used when working through a contextual joint‑work problem. Using a qualitative exploratory descriptive design, data were collected from students’ written solutions, think‑aloud explanations, and interview responses to capture their reasoning processes in depth. The participants were 15 first-semester students from the Mathematics Education Department, Universitas Islam Negeri (UIN) Mataram. Results showed four major categories of incorrect reasoning: intuitive reasoning based on misleading but salient information, additive reasoning that relied on differences rather than multiplicative structures, proportion attempts that identified proportional cues but applied them incorrectly, and other incomplete or unsupported strategies. Additive reasoning emerged as the most dominant pattern across students of varying proficiency, indicating a strong tendency to default to non‑proportional interpretations even when the situation required multiplicative thinking. Although some students recognized structural features such as periodic assistance, they struggled to coordinate unit work or rates, leading to systematically flawed conclusions. These findings suggest that students’ proportional reasoning errors stem from entrenched intuitive and additive tendencies. The study highlights the importance of instructional approaches that explicitly develop unit‑rate reasoning, strengthen multiplicative understanding, and support accurate representation of proportional situations.
Copyright (c) 2026 Samsul Irpan https://creativecommons.org/licenses/by-sa/4.0
Can Indonesia Eliminate Tuberculosis by 2030? A Deterministic Epidemic Model Approach
Indonesia, bearing the world’s second-highest tuberculosis (TB) burden, has mandated a national target to eliminate TB by 2030, aiming for an incidence rate of 65 per 100,000 population. This study aims not only to project future transmission dynamics but also to systematically explore the specific epidemiological barriers, namely, drug resistance and relapse mechanisms, that hinder achieving this goal. To address the heterogeneity of TB transmission, we developed a novel deterministic SVE3I3R model. This framework stratifies the population into vaccinated, latent Tuberculosis Infection (LTBI), and infectious compartments, explicitly distinguishing among Drug-Susceptible (DS-TB), Multidrug-Resistant (MDR-TB), and Extensively Drug-Resistant (XDR-TB) strains. The resulting system of ordinary differential equations was solved numerically using the fourth-order Runge-Kutta (RK4) method to ensure stability and accuracy in simulating long-term epidemiological trends from 2023 to 2030. Parameters were calibrated using national reports and literature specific to the Indonesian context. Projections indicate that Indonesia will miss the 2030 elimination target by a significant margin. The model forecasts a TB incidence rate of 321 per 100,000 population by 2030, nearly five times the national benchmark. The analysis reveals that failure to reach the target is mechanistically driven by a "relapse trap" among recovered individuals and an alarming exponential surge in resistant strains (MDR-TB and XDR-TB). These findings suggest that current control strategies are insufficient not merely in scale but in structure. Evidence-based policy must urgently shift from standard intervention to aggressive interruption of resistance pathways and enhanced management of the latent reservoir to prevent the projected demographic resurgence.
Copyright (c) 2026 Novi Reandy Sasmita https://creativecommons.org/licenses/by-sa/4.0
Analysis of the Spatial Error Model with Queen Contiguity Matrix Weights on Dengue Fever
Dengue Fever is one of the deadly diseases caused by a rapidly spreading virus transmitted through the Aedes aegypti mosquito. This study focuses on the NTB region, which has different geographical characteristics and infrastructure challenges. The variables used in this study are: dengue fever incidence, population, hospitals, community health centers, poor residents, and floods. The aim of this study is to model the factors that influence the occurrence of dengue fever in NTB. The method used is the Spatial Error Model (SEM), which serves to analyze spatial data to observe spatial correlation in the error variables. The research results indicate that the Moran Index and the Lagrange Multiplier test confirm the existence of spatial dependence in the error aspects. Significant variables at the 5% level affecting dengue fever cases are population size, the number of hospitals, and the number of community health centers. These findings provide an important scientific contribution as they represent one of the early studies that specifically identify and model the spatial dependence patterns of dengue fever cases in West Nusa Tenggara using a spatial econometric approach, thereby enriching the literature on spatial epidemiology at the regional level. The findings indicate that population growth and disparities in healthcare facilities increase the risk of dengue fever. This implies that more equitable spatial planning of healthcare services, strengthening of primary care, population density control, and increased community participation in sanitation and regular mosquito breeding site eradication are necessary as part of an to reduce dengue fever cases in NTB.
Copyright (c) 2026 Siti Soraya, Istin Fitriani Aziza, Rizwan Arizandi, Kirti Verma, Widani Darma Isasi, Suliadi Firdaus Sufahani https://creativecommons.org/licenses/by-sa/4.0